Various embodiments of fuel injection devices are known from the related art. In addition to magnetic injectors, piezoelectric multi-layer actuators are also used. In this connection, one advantage of piezoelectric actuators is that they are able to carry out deflections very quickly and precisely while simultaneously exercising great forces. One disadvantage of such piezoelectric actuators is, however, that the property degradation of the ceramic components of the piezoelectric actuator as a function of the number of electrical cycles makes a direct correlation of the applied voltage with the expansion of the piezoelectric actuator impossible. This prevents an exact determination of an actual needle position of a nozzle needle of the fuel injection device (needle lift characteristics) at any point in time of the injection process. Furthermore, the actual nozzle needle position in the nozzle seat is influenced by wear, carbon build-up, etc., which is impossible to detect in conventional fuel injection devices. For that reason, a measurement and coding is performed on each piezoelectric actuator before its installation. With the aid of this information, the particular stroke capability of an individual piezoelectric actuator is ascertained. This makes it possible to calculate a theoretical metering of the injected fuel quantity for each piezoelectric actuator. However, the fact that each individual piezoelectric actuator must be measured results in considerable manufacturing expense. Furthermore, the individual control units for the fuel injection device must also be adapted individually to the piezoelectric actuator. Moreover, the theoretically ascertained value may deviate significantly from later actual needle lift characteristics in the installed condition of the piezoelectric actuator. This results in inaccuracies in the injected fuel quantity. It would therefore be desirable to have a possibility for an exact needle position at each point in time of the injection process and to calculate from it a particular injected fuel quantity.